The 'Chandogya Upanishad' is one of the principal Upanishads, which are ancient Indian texts that form the basis of Hindu philosophy. The reason it is believed to have been composed in the 6th century B.C.E. is based on historical and textual analysis. Here's why:

Historical Context: The Upanishads are a group of texts that developed over a period of time, with many of them composed between the 8th century B.C.E. and the 6th century B.C.E. This period is often referred to as the Vedic period. The 'Chandogya Upanishad' is considered one of the earlier Upanishads, and its composition is generally associated with this Vedic period.

References within the Text: The 'Chandogya Upanishad' contains references to Vedic rituals and philosophical ideas that were prevalent during the Vedic period. These references provide historical context and suggest that it was composed during that time.

Tradition and Scholarship: Scholars and experts in the field of Indian philosophy and ancient texts have dated the 'Chandogya Upanishad' to the 6th century B.C.E. based on linguistic, philosophical, and historical analyses.

While it's important to note that dating ancient texts with precision can be challenging, the consensus among scholars and the historical context strongly support the 6th century B.C.E. as the period when the 'Chandogya Upanishad' was composed.